The transfer and stable homotopy theory

DOI10.1017/S0305004100054335zbMath0373.55011OpenAlexW2155755513MaRDI QIDQ4150851

Stewart B. Priddy, Daniel S. Kahn

Publication date: 1978

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100054335

Mathematics Subject Classification ID

Cohomology of groups (20J06) Homological methods in group theory (20J05) Applied homological algebra and category theory in algebraic topology (55U99) Stable homotopy groups (55Q10)

Related Items

Generic \(\mathcal A\)-generators for the polynomial algebra ⋮ The Whitehead conjecture and splitting 𝐵(𝐙/2)^{𝐤} ⋮ The transfer and James-Hopf invariants ⋮ James Maps, Segal Maps, and the Kahn-Priddy Theorem ⋮ Universal bounds for the exponent of stable homotopy groups ⋮ Exact Sequences of Spectra and Duality ⋮ Generators for the Bordism Algebra of Immersions ⋮ The triviality of the 61-stem in the stable homotopy groups of spheres ⋮ Homotopy Operations for Simplicial Commutative Algebras ⋮ A short proof of telescopic Tate vanishing ⋮ An Algebraic Analogue of a Conjecture of G. W. Whitehead ⋮ Some extensions in the Adams spectral sequence and the 51-stem ⋮ The period-index problem for twisted topological \(K\)-theory ⋮ The Kahn-Priddy Theorem and the homotopy of the three-sphere ⋮ The Whitehead conjecture, the tower ofS¹conjecture, and Hecke algebras of type A ⋮ Self-Maps of Loop Spaces. I ⋮ Self-Maps of Loop Spaces. II ⋮ Modular coinvariants and the modphomology ofQS^k ⋮ Additive Cohomology Operations ⋮ A filtration of spectra arising from families of subgroups of symmetric groups ⋮ Mahowald square and Adams differentials ⋮ Multiplicative transfers in ordinary cohomology ⋮ The image of Singer's fourth transfer ⋮ Tangential thickness of manifolds ⋮ Some comments on motivic nilpotence ⋮ Nonlinear analogs of linear group actions on spheres ⋮ The Kervaire invariant of immersions

Cites Work

• Homology of the infinite symmetric group
• The transfer map and fiber bundles
• Homotopy-everything 𝐻-spaces
• A Geometrical Observation on the Arf Invariant of a Framed Manifold
• Applications of the transfer to stable homotopy theory
• Homology of Iterated Loop Spaces
• A Generalization of the Transfer Map in the Cohomology of Groups
• Combinatorial homotopy. I